Options for new healers? Well, let's look at them in order of which classes I see as targets for the healer treatment:

Chemist -- Healer in many, many games. Very obvious option which has been suggested over 9000 times. Would almost certainly require a new class, however, due to needing a complete set of potion-making mechanics. Fortunately, second jobs are exceedingly easy to come by with that sort of design.
White Monk -- Healer for the Bangaa race in FFTA/2. Could be a second job for Pugilist, repurposing the Fists abilities. If not that, then you can be assured that White Monk won't make an appearance.
Oracle/Mystic -- Healing abilities in most appearances (Banon, FF5 port). That's never really the point of the job, but it's no less possible than Scholar as fairy-summoning healer. Could come from any caster, which would have to be Thaumaturge at this point or some future caster. I don't know how you'd implement a Thaumaturge healer, though. Would have to tie healing rate to Transpose use, which is a bit fuzzy with current 10s CD on Transpose.
Devout/Seer -- Sometimes a superior white mage, Seer has become a status protection mage in more recent entries. This could be a healer's schtick and all, but doing so wouldn't make much sense without an entirely new class dedicated to it. Might be a bit odd to call something Seer with Gridanian storyline involving Conjurerers.

With some liberties, you could also do these:

Puppetmaster -- Healing abilities in FF4: After Years, FF11. Could come from any class. Would be a bit lame to have two pet healers, though.
Dancer -- Has had many a healing dance in its day, but is never a healer, per se. Could come from any lightly-armored character, which is just Pugilist or Archer at this point but could be other future classes as well. Yeah, I've now made two suggestions of PGL healer, so sue me.
Machinist -- Healing ability in FFTA/2, but it's a bit of a stretch.

I have omitted a few options for various reasons. Bishop is just a white mage in different clothing rather than a unique design. I thought Mediator/Orator would be a cool one with Musketeer, but it has no history of healing abilities. Sage carries great healing prowess, but isn't much of a Sage without the other side of the coin. Red Mage is like Sage, except that it also has melee abilities, which makes it a pretty terrible candidate in general.